I have not found a source referencing Fionn ever battling Nuadu, but I'm also open to being wrong - I am not as strong in the Finn Cycle as I am in the Ulster and Mythological Cycle.Mm'kay, interesting. Although I will clarify that Fionn's F/GO profile references him fighting Aillen and Nuada as two separate instances over the course of his life so it doesn't appear that they are confusing the two at the least.
(One day I will finish this stupid document for a Lostbelt based on medieval Ireland.)